
F stands for the resultant force, in Newtons, acting on a particle,
m is the mass in kilograms of the particle
a is the acceleration in m/s² produced.
Newton's law can be applied in force diagrams to find various forces acting on a particle.
Summary/Background

Newton's laws of motion are three physical laws which provide relationships between the forces acting on a body and the motion of the body, first compiled by Sir Isaac Newton. Newton's laws were first published together in his work Philosophiae Naturalis Principia Mathematica (1687). The Principia is recognised as the greatest scientific book ever written. Newton analysed the motion of bodies in resisting and non-resisting media under the action of centripetal forces. The results were applied to orbiting bodies, projectiles, pendulums, and free-fall near the Earth. He further demonstrated that the planets were attracted toward the Sun by a force varying as the inverse square of the distance and generalised that all heavenly bodies mutually attract one another.
The laws form the basis for classical mechanics.
- Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it.
- The relationship between an object's mass m, its acceleration a, and the applied force F is F = ma. Acceleration and force are vectors (as indicated by their symbols being displayed in slant bold font); in this law the direction of the force vector is the same as the direction of the acceleration vector.
- For every action there is an equal and opposite reaction.
Software/Applets used on this page
Glossary
acceleration
the rate of change of velocity with time. It is a vector quantity with magnitude and direction.
body
an object with both mass and size that cannot be taken to be a particle
calculus
the study of change; a major branch of mathematics that includes the study of limits, derivatives, rates of change, gradient, integrals, area, summation, and infinite series. Historically, it has been referred to as "the calculus of infinitesimals", or "infinitesimal calculus".
There are widespread applications in science, economics, and engineering.
There are widespread applications in science, economics, and engineering.
centripetal
of a force directed towards the centre in circular motion
force
that which causes a body to accelerate or change in momentum
integral
the anti-derivative
mass
a measure of the quantity of matter in an object
newton
the unit of force
particle
an object with negligible size and internal structure, which can be represented by a point; the fundamental assumption in mechanics.
union
The union of two sets A and B is the set containing all the elements of A and B.
vector
A mathematical object with magnitude and direction.
work
Equal to F x s, where F is the force in Newtons and s is the distance travelled and is measured in Joules.
This question appears in the following syllabi:
Syllabus | Module | Section | Topic | Exam Year |
---|---|---|---|---|
AQA A-Level (UK - Pre-2017) | M1 | Dynamics | Newton's Laws | - |
AQA AS Maths 2017 | Mechanics | Forces and Newton's Laws | Newton's Laws | - |
AQA AS/A2 Maths 2017 | Mechanics | Forces and Newton's Laws | Newton's Laws | - |
CCEA A-Level (NI) | M1 | Dynamics | Newton's Laws | - |
CIE A-Level (UK) | M1 | Dynamics | Newton's Laws | - |
Edexcel A-Level (UK - Pre-2017) | M1 | Dynamics | Newton's Laws | - |
Edexcel AS Maths 2017 | Mechanics | Forces and Newton's Laws | Newton's Laws | - |
Edexcel AS/A2 Maths 2017 | Mechanics | Forces and Newton's Laws | Newton's Laws | - |
OCR A-Level (UK - Pre-2017) | M1 | Dynamics | Newton's Laws | - |
OCR AS Maths 2017 | Mechanics | Forces and Newton's Laws | Newton's Laws | - |
OCR MEI AS Maths 2017 | Mechanics | Forces and Newton's Laws | Newton's Laws | - |
OCR-MEI A-Level (UK - Pre-2017) | M1 | Dynamics | Newton's Laws | - |
Pre-U A-Level (UK) | Mech | Dynamics | Newton's Laws | - |
Universal (all site questions) | D | Dynamics | Newton's Laws | - |
WJEC A-Level (Wales) | M1 | Dynamics | Newton's Laws | - |